Eight cubes

Probability Level 3

You have eight cubic blocks, 4 red and 4 green.

How many ways can you arrange them in a 2 × 2 × 2 2\times 2\times 2 cube such that no red block is placed on top of a green block?

Clarification : The answer should include all rotations and reflections.

Image credit : http://www.cubecompany.co.uk


The answer is 19.

Geoff Pilling by Geoff Pilling , 53, USA

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1 solution

Geoff Pilling
Sep 24, 2018

There is 1 way to do it with 4 red blocks on the bottom, 12 ways to do it with 3 red blocks on the bottom, and 6 ways to do it with two red blocks on the bottom.

1 + 12 + 6 = 19 1 + 12 + 6 = \boxed{19}

4 Helpful 0 Interesting 0 Brilliant 0 Confused

The questions states that the number of possibilities is independent of rotation but your answer doesn't take this into account. For example I only see 2 ways to do it with two red blocks on bottom:

way 1: top and bottom are both
r r
g g

way 2: top and bottom are both
r g
g r

The final answer I got was 6 (if only allowing rotations about the vertical axis) or 5 (if all rotations are allowed).

Nate Jellis - 2 years, 8 months ago

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Good point... I updated the verbiage a bit... Any suggestions on how I can make my intent clearer?

Geoff Pilling - 2 years, 8 months ago

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